On a product of positive semidefinite matrices (Q1124938)

The matrix \(A\) is said to be positive semidefinite (psd) if there exists a matrix \(P\) such that \(PP^*=A\). If \(A\) and its conjugate transpose \(A^*\) have the same range space, then \(A\) is called EP. Necessary and sufficient conditions are given for the product of two positive semidefinite (psd) matrices to be EP. As a consequence, it is shown that the product of two psd matrices is psd if and only if the product is normal.